Uniqueness of Bounded Solutions for the Homogeneous Landau Equation with a Coulomb Potential

Nicolas Fournier (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We prove the uniqueness of bounded solutions for the spatially homogeneous Fokker-Planck-Landau equation with a Coulomb potential. Since the local (in time) existence of such solutions has been proved by Arsen'ev-Peskov (Z. Vycisl. Mat. i Mat. Fiz. 17:1063-1068, 1977), we deduce a local well-posedness result. The stability with respect to the initial condition is also checked.

Domaines: Physique Classique [physics.class-ph]

Nicolas Fournier. Uniqueness of Bounded Solutions for the Homogeneous Landau Equation with a Coulomb Potential. Communications in Mathematical Physics, 2010, 299 (3), pp.765--782. ⟨10.1007/s00220-010-1113-9⟩. ⟨hal-00693006⟩